Cut a horizontal slit in center of each chicken breast, cutting in as far as possible without cutting through, to make a pocket.
In a small bowl, mix together goat cheese and Neufchâtel cheese. Stuff cheese mixture into each breast, pressing mixture evenly with fingers. Insert about 7 cherries into each breast and then secure opening with toothpicks to prevent leaking during cooking.
Preheat grill or grease a grill pan and heat over medium heat. Add chicken and cook, covered, for 15 minutes, turning once. Remove toothpicks before serving. Garnish with fresh cherries.